Finding Equations of Exponential Functions

This video tutorial by Kirk Wier focuses on writing equations of exponential functions, extending concepts from Algebra 1. It covers determining values of A and B, solving systems of equations, and graphing exponential functions. The lesson includes exercises and a multiple-choice problem to reinforce learning. The tutorial emphasizes understanding exponent properties and using them to solve for unknowns in exponential equations.

What is the form of the exponential function discussed in the lesson?

• f(x) = a * bx

• f(x) = a + bx

• f(x) = a * b^x

• f(x) = ax / b

What does the variable 'a' represent in the exponential function?

• The base of the exponent

• The coefficient of x

• The y-intercept of the function

• The slope of the function

What does the variable 'B' represent in the exponential function?

• The y-intercept

• The exponent's base

• The variable x's coefficient

• The multiplier when x increases by 1

How do you determine the value of 'B' when given two points on the function?

• Divide the y-values and solve for B

• Multiply the y-values and solve for B

• Add the y-values and solve for B

• Subtract the y-values and solve for B

In the example with F(0) = 8 and F(3) = 1000, what is the value of 'a'?

• 8

• 1000

• 3

• 0

How is the base 'B' determined when the function values at two different x-values are known?

• By taking the cube root of the ratio of the function values

• By taking the square root of the ratio of the function values

• By squaring the ratio of the function values

• By taking the fourth root of the ratio of the function values

What method is used to eliminate the constant 'a' when solving a system of exponential equations?

• Addition of equations

• Subtraction of equations

• Division of equations

• Multiplication of equations

What technique is applied to solve for 'B' when a system of exponential equations is given?

• Using quadratic formula

• Using linear equations

• Using logarithms

• Using properties of exponents

What is the growth rate of the bacterial colony per hour, as modeled in the lesson?

• 14%

• 10%

• 12%

• 16%

What is the final form of the exponential function used to model the bacterial colony's growth?

• y = 98 * 1.04^x

• y = 58 * 1.14^x

• y = 98 * 1.14^x

• y = 58 * 1.04^x